Families of birth-death processes with similar time-dependent behaviour.

R.B. Lenin, P.R. Parthasarathy, Willem R.W. Scheinhardt, Erik A. van Doorn

Research output: Contribution to journalArticleAcademicpeer-review

16 Citations (Scopus)

Abstract

We consider birth-death processes taking values in N ≡ {0,1,... }, but allow the death rate in state 0 to be positive, so that escape from N is possible. Two such processes with transition functions { pij(t) } and { ̃pij(t) } are said to be similar if, for all i, j ∈ N, there are constants cij such that ̃pij(t) = cijpij(t) for all t ≥ 0. We determine conditions on the birth and death rates of a birth-death process for the process to be a member of a family of similar processes, and we identify the members of such a family. These issues are also resolved in the more general setting in which the two processes are called similar if there are constants cij and ν such that ̃pij(t) = cijeνtpij(t) for all t ≥ 0.
Original languageUndefined
Article number10.1239/jap/1014842840
Pages (from-to)835-849
Number of pages14
JournalJournal of applied probability
Volume2000
Issue number37
DOIs
Publication statusPublished - 2000

Keywords

  • invariant vector
  • EWI-12851
  • transition function
  • METIS-140634
  • Transient behaviour
  • IR-62348
  • Chain sequence
  • Absorption probability

Cite this

Lenin, R. B., Parthasarathy, P. R., Scheinhardt, W. R. W., & van Doorn, E. A. (2000). Families of birth-death processes with similar time-dependent behaviour. Journal of applied probability, 2000(37), 835-849. [10.1239/jap/1014842840]. https://doi.org/10.1239/jap/1014842840